Interferometric imaging, and more in particular holographic interferometry, offers a variety of applications. Holography is generally defined as the storage and reconstruction of wave fields by the recording of their interference pattern. Specifically, in holographic imaging, holograms are generally formed by recording the interference pattern of a coherent beam scattered by an object (object beam) and a coherent reference beam non-scattered by the object (reference beam). Holography with non-coherent light has also been demonstrated, but its use is less common. In conventional analog holography, holograms are recorded in photographic material, such as photographic film or plates, and the image of the object is usually reconstructed by illuminating the hologram with the same coherent reference beam. In digital holography, holograms are recorded by a detector array, such as a charge-coupled device (CCD) or a complementary metal-oxide semiconductor (CMOS) sensor, and the image of the object is reconstructed by a computer using numerical algorithms. The major advantage of digital holography is that it avoids the use of chemical photographic material, avoids photographic processing, and—with the latest advances in computing technology and processing techniques—holographic images can be recorded and reconstructed in substantially real time.
Off-axis holography is a commonly used digital holographic technique. In off-axis holography, the reference beam is angularly tilted with reference to object beam (the optical axis of the object beam incident on the object). Among other applications, off-axis holography has been used in precision measurements for determining particle size, polarization or coherence of light, phase-contrast, synthetic aperture, time-of-flight in optical coherence tomography (OCT), and for three-dimensional (3D) imaging. An important application of 3D imaging is the measurement of the shape of objects both in large and small scale. For example, holographic interferometry has been used to obtain 3D images of large objects, such as a car or a human body, or small objects, such as live cells or molecular particles within cells.
Another commonly used holographic technique is phase-shifting holography, where the reference beam is inline (or on-axis) with reference with the object beam. In general, 3 or 4 images are recorded with a phase difference of 2π/3 or π/2, respectively, between each image. Recording a hologram inline requires a very accurate phase shift between consecutive images since the conjugate image alias overlaps with the true image. Thus, image aliases are suppressed by subtracting the conjugate image from the true image. Applications for phase-shifting holography are substantially similar to those for on-axis holography. Indeed, some applications that use a combination of off-axis and phase-shifting holography have been proposed. See, for example, “Noise and aliases in off-axis and phase-shifting holography” by Gross et al., Applied Optics, Vol. 47, No. 11, April 2008.
In holographic interferometry, in particular when using coherent illumination, an important aspect of research is focused on attempts to improve image quality by minimizing speckle noise. Specifically, because of the coherent illumination, the coherent noise or speckle (speckle noise), which originates from rough surfaces of the sample, refractive inhomogeneities of optics, multiple beam reflections, dust particles and the like, degrades the image quality and measurement accuracy. Numerous techniques have been previously proposed for mitigating speckle noise. Spatial or digital filtering methods, such as discrete Fourier filtering, Wiener filtering and wavelet filtering are well known. Filtering techniques may disadvantageously reduce image resolution. Other known methods include recording multiple holograms and superposing multiple reconstructed images with different speckle patterns. The multiple holograms may be obtained using different optical configurations including, for example, using multiple wavelengths, changing the incident angle of illumination, changing the polarization of illumination, using multi-angle tilted illumination, and others. Representative examples of techniques used to reduce speckle noise with their respective shortcomings are summarized below.
Yong-Keun Park et al., (hereinafter “Park”), in an article entitled “Speckle-field digital holographic microscopy”, published by Optics Express 17 (15), 12285, July 2009, describes a technique of extracting a sample-induced phase delay with speckle illumination. Specifically, Park generated a speckle field by illuminating a holographic diffuser with a laser. The speckle field traveled through a microscope and was imaged on a detector. The hologram of the speckle field was generated by imposing a plane-wave reference beam on the detector. Using a heterodyne Mach-Zehnder interferometer, a complex E-field of the speckle was retrieved. Then, a sample (a polystyrene bead of 10 μm diameter) submerged in immersion oil was placed on a sample stage of the interferometer with the same speckle field illumination. Introducing the sample into the interferometer modified the original speckle pattern. Next, the E-field of the modified speckle was recorded in the same way as the recording of the original speckle pattern. In the obtained images, the sample is almost invisible because its image is overlapped with the complex pattern of the speckle field. It should be noted that with this technique the speckle is stationary, as the coherence length of the laser is much larger than the scattering length of the diffuser. Therefore, the background speckle field can be removed and the sample-induced complex field image can be retrieved from the speckle field by dividing it by the field without the sample. Purportedly, this technique can produce clear images of the sample.
However, since Park's disclosed technique relies on the premise that the background (phase image taken without the sample) can be successfully subtracted from the signal (phase image taken with the sample), this technique is not easily applicable for complicated samples larger than a single bead or a single cell. The reason for the difficulty is that inserting the sample is likely to change the speckle seen by the detector which makes the background subtraction very challenging if not impossible. In addition, since Park's disclosed technique is applied in the phase shifting configuration, it is very impractical in the off-axis configuration which requires spatial coherence. The off-axis configuration is highly desirable for high-speed tomographic phase imaging, for example. Therefore, although Park's technique is in principle feasible, it appears to be not practical for commercial applications, such as for high-speed tomographic phase imaging.
Feng Pan et al., (hereinafter “Pan”), in an article entitled “Coherent Noise Reduction In Digital Holographic Phase Contrast Microscopy by Slightly Shifting Object”, published by Optics Express 19 (5), 3862, February 2011, discloses a method to reduce coherent noise in digital holographic phase contrast microscopy. According to Pan, by slightly shifting the sample in a lateral direction, a series of digital holograms with different coherent noise patterns is recorded. Each hologram is reconstructed individually, while the different phase tilts of the reconstructed complex amplitudes due to the specimen shifts are corrected in the hologram plane by using a numerical parametric lens method. Afterwards, the lateral displacements of the phase maps from different holograms are compensated in the image plane by using a digital image registration method. Thus, all phase images have the same distribution, but uncorrelated coherent noise patterns. By a proper averaging procedure, the coherent noise of phase contrast image is reduced significantly.
In the method disclosed by Pan, the reduction of the speckle noise is achieved by averaging the phase images taken at different lateral positions. Specifically, if positions are far apart so that the speckle patterns are decorrelated, the averaged image will tend to reveal the signal while the speckle noise is suppressed. The problem with Pan's proposed method is that in order to make sure that the speckle patterns are decorrelated, the amount of each lateral shift of the sample needs to be larger than several microns (μm). Specifically, according to Pan's published results, approximately 5 μm per shift is necessary to reduce the correlation coefficient to less than 0.07. Therefore, for an average of 25 images (5×5), a shift of at least 20 μm×20 μm is required. This will significantly reduce the field of view (FOV), in particular in microscopy where the FOV can be as little as 100 μm. In addition, the aberration, which can be in the form of phase gradient either linearly or spherically depending on the lateral position, is likely to be different for each image taken at the different lateral positions. This makes the aberration correction for each image difficult to be consistent.
International publication WO 2010/096634, published under the Patent Corporation Treaty (PCT) and disclosed by Robert F. Dillon et al. (hereinafter “Dillon”), discloses a technique entitled “Speckle Noise Reduction for a Coherent Illumination Imaging System”. Dillon's method includes illuminating an object with coherent radiation at a plurality of angular orientations, acquiring an image of the illuminated object at each of the angular orientations, and summing the images of the illuminated object at each of the plural angular orientations to generate an image of the illuminated object having reduced speckle noise. However, it is seen that Dillon's method is namely directed to removing the speckle noise from intensity imaging, and may be inappropriate for phase imaging.
What is needed, therefore, is a technique that can overcome the above-noted shortcomings and reliably and accurately reduce speckle noise in a simple and efficient manner for both phase and amplitude (intensity) images.